TSTP Solution File: SEU281+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU281+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 08:48:26 EDT 2022
% Result : Theorem 39.07s 19.68s
% Output : Proof 62.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU281+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 19 02:55:14 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.57 ____ _
% 0.18/0.57 ___ / __ \_____(_)___ ________ __________
% 0.18/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.18/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.18/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.18/0.57
% 0.18/0.57 A Theorem Prover for First-Order Logic
% 0.18/0.57 (ePrincess v.1.0)
% 0.18/0.57
% 0.18/0.57 (c) Philipp Rümmer, 2009-2015
% 0.18/0.57 (c) Peter Backeman, 2014-2015
% 0.18/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.18/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.18/0.57 Bug reports to peter@backeman.se
% 0.18/0.57
% 0.18/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.18/0.57
% 0.18/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.65/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.45/0.91 Prover 0: Preprocessing ...
% 1.80/1.09 Prover 0: Warning: ignoring some quantifiers
% 1.96/1.11 Prover 0: Constructing countermodel ...
% 2.22/1.27 Prover 0: gave up
% 2.22/1.27 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.61/1.29 Prover 1: Preprocessing ...
% 2.85/1.38 Prover 1: Warning: ignoring some quantifiers
% 2.85/1.39 Prover 1: Constructing countermodel ...
% 3.44/1.51 Prover 1: gave up
% 3.44/1.51 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.44/1.53 Prover 2: Preprocessing ...
% 3.88/1.61 Prover 2: Warning: ignoring some quantifiers
% 4.06/1.61 Prover 2: Constructing countermodel ...
% 4.56/1.79 Prover 2: gave up
% 4.56/1.79 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.89/1.81 Prover 3: Preprocessing ...
% 4.89/1.83 Prover 3: Warning: ignoring some quantifiers
% 4.89/1.83 Prover 3: Constructing countermodel ...
% 4.89/1.87 Prover 3: gave up
% 4.89/1.87 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 5.26/1.88 Prover 4: Preprocessing ...
% 5.48/1.95 Prover 4: Warning: ignoring some quantifiers
% 5.48/1.96 Prover 4: Constructing countermodel ...
% 9.63/2.93 Prover 4: gave up
% 9.63/2.93 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 9.63/2.94 Prover 5: Preprocessing ...
% 9.63/2.97 Prover 5: Warning: ignoring some quantifiers
% 9.63/2.97 Prover 5: Constructing countermodel ...
% 10.20/3.04 Prover 5: gave up
% 10.20/3.04 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 10.20/3.05 Prover 6: Preprocessing ...
% 10.20/3.09 Prover 6: Warning: ignoring some quantifiers
% 10.20/3.09 Prover 6: Constructing countermodel ...
% 10.68/3.18 Prover 6: gave up
% 10.68/3.18 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 10.68/3.19 Prover 7: Preprocessing ...
% 11.09/3.21 Prover 7: Proving ...
% 29.55/13.40 Prover 8: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 29.55/13.43 Prover 8: Preprocessing ...
% 29.55/13.47 Prover 8: Proving ...
% 39.07/19.67 Prover 8: proved (6272ms)
% 39.07/19.68 Prover 7: stopped
% 39.07/19.68
% 39.07/19.68 % SZS status Theorem for theBenchmark
% 39.07/19.68
% 39.07/19.68 Generating proof ... found it (size 64)
% 62.21/37.24
% 62.21/37.24 % SZS output start Proof for theBenchmark
% 62.21/37.24 Assumed formulas after preprocessing and simplification:
% 62.21/37.24 | (0) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordinal(v2) = v1) | ~ (ordinal(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (epsilon_transitive(v2) = v1) | ~ (epsilon_transitive(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (epsilon_connected(v2) = v1) | ~ (epsilon_connected(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (cartesian_product2(v0, v1) = v2) | ? [v3] : ( ! [v4] : ! [v5] : (v5 = 0 | ~ (in(v4, v3) = v5) | ~ (in(v4, v2) = 0) | ! [v6] : ! [v7] : ( ~ (ordered_pair(v6, v7) = v4) | ? [v8] : ? [v9] : (singleton(v6) = v9 & in(v6, v0) = v8 & ( ~ (v9 = v7) | ~ (v8 = 0))))) & ! [v4] : ( ~ (in(v4, v3) = 0) | (in(v4, v2) = 0 & ? [v5] : ? [v6] : (singleton(v5) = v6 & ordered_pair(v5, v6) = v4 & in(v5, v0) = 0))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (ordinal(v0) = v1) | ? [v2] : ? [v3] : (epsilon_transitive(v0) = v2 & epsilon_connected(v0) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ! [v0] : ! [v1] : ( ~ (ordinal(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (empty(v0) = v2 & epsilon_transitive(v0) = v3 & epsilon_connected(v0) = v4 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0 & v1 = 0)))) & ! [v0] : ( ~ (ordinal(v0) = 0) | (epsilon_transitive(v0) = 0 & epsilon_connected(v0) = 0)) & ? [v0] : ? [v1] : ? [v2] : (cartesian_product2(v0, v1) = v2 & ! [v3] : ? [v4] : ? [v5] : ? [v6] : (in(v4, v3) = v5 & in(v4, v2) = v6 & ( ~ (v6 = 0) | ~ (v5 = 0) | ! [v7] : ! [v8] : ( ~ (ordered_pair(v7, v8) = v4) | ? [v9] : ? [v10] : (singleton(v7) = v10 & in(v7, v0) = v9 & ( ~ (v10 = v8) | ~ (v9 = 0))))) & (v5 = 0 | (v6 = 0 & ? [v7] : ? [v8] : (singleton(v7) = v8 & ordered_pair(v7, v8) = v4 & in(v7, v0) = 0))))) & ? [v0] : ? [v1] : ( ~ (v1 = 0) & empty(v0) = v1 & ordinal(v0) = 0 & epsilon_transitive(v0) = 0 & epsilon_connected(v0) = 0) & ? [v0] : ? [v1] : ( ~ (v1 = 0) & empty(v0) = v1) & ? [v0] : empty(v0) = 0 & ? [v0] : (ordinal(v0) = 0 & epsilon_transitive(v0) = 0 & epsilon_connected(v0) = 0)
% 62.21/37.26 | Applying alpha-rule on (0) yields:
% 62.21/37.26 | (1) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 62.21/37.26 | (2) ? [v0] : (ordinal(v0) = 0 & epsilon_transitive(v0) = 0 & epsilon_connected(v0) = 0)
% 62.21/37.26 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (epsilon_connected(v2) = v1) | ~ (epsilon_connected(v2) = v0))
% 62.21/37.26 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordinal(v2) = v1) | ~ (ordinal(v2) = v0))
% 62.21/37.27 | (5) ? [v0] : ? [v1] : ( ~ (v1 = 0) & empty(v0) = v1)
% 62.21/37.27 | (6) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (epsilon_transitive(v2) = v1) | ~ (epsilon_transitive(v2) = v0))
% 62.21/37.27 | (7) ? [v0] : ? [v1] : ? [v2] : (cartesian_product2(v0, v1) = v2 & ! [v3] : ? [v4] : ? [v5] : ? [v6] : (in(v4, v3) = v5 & in(v4, v2) = v6 & ( ~ (v6 = 0) | ~ (v5 = 0) | ! [v7] : ! [v8] : ( ~ (ordered_pair(v7, v8) = v4) | ? [v9] : ? [v10] : (singleton(v7) = v10 & in(v7, v0) = v9 & ( ~ (v10 = v8) | ~ (v9 = 0))))) & (v5 = 0 | (v6 = 0 & ? [v7] : ? [v8] : (singleton(v7) = v8 & ordered_pair(v7, v8) = v4 & in(v7, v0) = 0)))))
% 62.21/37.27 | (8) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 62.21/37.27 | (9) ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 62.21/37.27 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3))
% 62.21/37.27 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0))
% 62.21/37.27 | (12) ! [v0] : ( ~ (ordinal(v0) = 0) | (epsilon_transitive(v0) = 0 & epsilon_connected(v0) = 0))
% 62.21/37.27 | (13) ? [v0] : empty(v0) = 0
% 62.21/37.27 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (cartesian_product2(v0, v1) = v2) | ? [v3] : ( ! [v4] : ! [v5] : (v5 = 0 | ~ (in(v4, v3) = v5) | ~ (in(v4, v2) = 0) | ! [v6] : ! [v7] : ( ~ (ordered_pair(v6, v7) = v4) | ? [v8] : ? [v9] : (singleton(v6) = v9 & in(v6, v0) = v8 & ( ~ (v9 = v7) | ~ (v8 = 0))))) & ! [v4] : ( ~ (in(v4, v3) = 0) | (in(v4, v2) = 0 & ? [v5] : ? [v6] : (singleton(v5) = v6 & ordered_pair(v5, v6) = v4 & in(v5, v0) = 0)))))
% 62.21/37.27 | (15) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0))
% 62.21/37.27 | (16) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 62.21/37.27 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 62.21/37.27 | (18) ! [v0] : ! [v1] : (v1 = 0 | ~ (ordinal(v0) = v1) | ? [v2] : ? [v3] : (epsilon_transitive(v0) = v2 & epsilon_connected(v0) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 62.21/37.27 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 62.21/37.27 | (20) ! [v0] : ! [v1] : ( ~ (ordinal(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (empty(v0) = v2 & epsilon_transitive(v0) = v3 & epsilon_connected(v0) = v4 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0 & v1 = 0))))
% 62.21/37.27 | (21) ? [v0] : ? [v1] : ( ~ (v1 = 0) & empty(v0) = v1 & ordinal(v0) = 0 & epsilon_transitive(v0) = 0 & epsilon_connected(v0) = 0)
% 62.21/37.27 |
% 62.21/37.27 | Instantiating (7) with all_9_0_6, all_9_1_7, all_9_2_8 yields:
% 62.21/37.27 | (22) cartesian_product2(all_9_2_8, all_9_1_7) = all_9_0_6 & ! [v0] : ? [v1] : ? [v2] : ? [v3] : (in(v1, v0) = v2 & in(v1, all_9_0_6) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0) | ! [v4] : ! [v5] : ( ~ (ordered_pair(v4, v5) = v1) | ? [v6] : ? [v7] : (singleton(v4) = v7 & in(v4, all_9_2_8) = v6 & ( ~ (v7 = v5) | ~ (v6 = 0))))) & (v2 = 0 | (v3 = 0 & ? [v4] : ? [v5] : (singleton(v4) = v5 & ordered_pair(v4, v5) = v1 & in(v4, all_9_2_8) = 0))))
% 62.21/37.27 |
% 62.21/37.27 | Applying alpha-rule on (22) yields:
% 62.21/37.27 | (23) cartesian_product2(all_9_2_8, all_9_1_7) = all_9_0_6
% 62.21/37.28 | (24) ! [v0] : ? [v1] : ? [v2] : ? [v3] : (in(v1, v0) = v2 & in(v1, all_9_0_6) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0) | ! [v4] : ! [v5] : ( ~ (ordered_pair(v4, v5) = v1) | ? [v6] : ? [v7] : (singleton(v4) = v7 & in(v4, all_9_2_8) = v6 & ( ~ (v7 = v5) | ~ (v6 = 0))))) & (v2 = 0 | (v3 = 0 & ? [v4] : ? [v5] : (singleton(v4) = v5 & ordered_pair(v4, v5) = v1 & in(v4, all_9_2_8) = 0))))
% 62.21/37.28 |
% 62.21/37.28 | Instantiating formula (14) with all_9_0_6, all_9_1_7, all_9_2_8 and discharging atoms cartesian_product2(all_9_2_8, all_9_1_7) = all_9_0_6, yields:
% 62.21/37.28 | (25) ? [v0] : ( ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v1, v0) = v2) | ~ (in(v1, all_9_0_6) = 0) | ! [v3] : ! [v4] : ( ~ (ordered_pair(v3, v4) = v1) | ? [v5] : ? [v6] : (singleton(v3) = v6 & in(v3, all_9_2_8) = v5 & ( ~ (v6 = v4) | ~ (v5 = 0))))) & ! [v1] : ( ~ (in(v1, v0) = 0) | (in(v1, all_9_0_6) = 0 & ? [v2] : ? [v3] : (singleton(v2) = v3 & ordered_pair(v2, v3) = v1 & in(v2, all_9_2_8) = 0))))
% 62.21/37.28 |
% 62.21/37.28 | Instantiating (25) with all_18_0_12 yields:
% 62.21/37.28 | (26) ! [v0] : ! [v1] : (v1 = 0 | ~ (in(v0, all_18_0_12) = v1) | ~ (in(v0, all_9_0_6) = 0) | ! [v2] : ! [v3] : ( ~ (ordered_pair(v2, v3) = v0) | ? [v4] : ? [v5] : (singleton(v2) = v5 & in(v2, all_9_2_8) = v4 & ( ~ (v5 = v3) | ~ (v4 = 0))))) & ! [v0] : ( ~ (in(v0, all_18_0_12) = 0) | (in(v0, all_9_0_6) = 0 & ? [v1] : ? [v2] : (singleton(v1) = v2 & ordered_pair(v1, v2) = v0 & in(v1, all_9_2_8) = 0)))
% 62.21/37.28 |
% 62.21/37.28 | Applying alpha-rule on (26) yields:
% 62.21/37.28 | (27) ! [v0] : ! [v1] : (v1 = 0 | ~ (in(v0, all_18_0_12) = v1) | ~ (in(v0, all_9_0_6) = 0) | ! [v2] : ! [v3] : ( ~ (ordered_pair(v2, v3) = v0) | ? [v4] : ? [v5] : (singleton(v2) = v5 & in(v2, all_9_2_8) = v4 & ( ~ (v5 = v3) | ~ (v4 = 0)))))
% 62.21/37.28 | (28) ! [v0] : ( ~ (in(v0, all_18_0_12) = 0) | (in(v0, all_9_0_6) = 0 & ? [v1] : ? [v2] : (singleton(v1) = v2 & ordered_pair(v1, v2) = v0 & in(v1, all_9_2_8) = 0)))
% 62.21/37.28 |
% 62.21/37.28 | Introducing new symbol ex_30_0_13 defined by:
% 62.21/37.28 | (29) ex_30_0_13 = all_18_0_12
% 62.21/37.28 |
% 62.21/37.28 | Instantiating formula (24) with ex_30_0_13 yields:
% 62.21/37.28 | (30) ? [v0] : ? [v1] : ? [v2] : (in(v0, ex_30_0_13) = v1 & in(v0, all_9_0_6) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ! [v3] : ! [v4] : ( ~ (ordered_pair(v3, v4) = v0) | ? [v5] : ? [v6] : (singleton(v3) = v6 & in(v3, all_9_2_8) = v5 & ( ~ (v6 = v4) | ~ (v5 = 0))))) & (v1 = 0 | (v2 = 0 & ? [v3] : ? [v4] : (singleton(v3) = v4 & ordered_pair(v3, v4) = v0 & in(v3, all_9_2_8) = 0))))
% 62.21/37.28 |
% 62.21/37.28 | Instantiating (30) with all_31_0_14, all_31_1_15, all_31_2_16 yields:
% 62.21/37.28 | (31) in(all_31_2_16, ex_30_0_13) = all_31_1_15 & in(all_31_2_16, all_9_0_6) = all_31_0_14 & ( ~ (all_31_0_14 = 0) | ~ (all_31_1_15 = 0) | ! [v0] : ! [v1] : ( ~ (ordered_pair(v0, v1) = all_31_2_16) | ? [v2] : ? [v3] : (singleton(v0) = v3 & in(v0, all_9_2_8) = v2 & ( ~ (v3 = v1) | ~ (v2 = 0))))) & (all_31_1_15 = 0 | (all_31_0_14 = 0 & ? [v0] : ? [v1] : (singleton(v0) = v1 & ordered_pair(v0, v1) = all_31_2_16 & in(v0, all_9_2_8) = 0)))
% 62.21/37.28 |
% 62.21/37.28 | Applying alpha-rule on (31) yields:
% 62.21/37.28 | (32) in(all_31_2_16, ex_30_0_13) = all_31_1_15
% 62.21/37.28 | (33) in(all_31_2_16, all_9_0_6) = all_31_0_14
% 62.21/37.28 | (34) ~ (all_31_0_14 = 0) | ~ (all_31_1_15 = 0) | ! [v0] : ! [v1] : ( ~ (ordered_pair(v0, v1) = all_31_2_16) | ? [v2] : ? [v3] : (singleton(v0) = v3 & in(v0, all_9_2_8) = v2 & ( ~ (v3 = v1) | ~ (v2 = 0))))
% 62.21/37.28 | (35) all_31_1_15 = 0 | (all_31_0_14 = 0 & ? [v0] : ? [v1] : (singleton(v0) = v1 & ordered_pair(v0, v1) = all_31_2_16 & in(v0, all_9_2_8) = 0))
% 62.21/37.28 |
% 62.21/37.28 +-Applying beta-rule and splitting (35), into two cases.
% 62.21/37.28 |-Branch one:
% 62.63/37.28 | (36) all_31_1_15 = 0
% 62.63/37.28 |
% 62.63/37.29 | From (36) and (32) follows:
% 62.63/37.29 | (37) in(all_31_2_16, ex_30_0_13) = 0
% 62.63/37.29 |
% 62.63/37.29 | Instantiating formula (28) with all_31_2_16 yields:
% 62.63/37.29 | (38) ~ (in(all_31_2_16, all_18_0_12) = 0) | (in(all_31_2_16, all_9_0_6) = 0 & ? [v0] : ? [v1] : (singleton(v0) = v1 & ordered_pair(v0, v1) = all_31_2_16 & in(v0, all_9_2_8) = 0))
% 62.63/37.29 |
% 62.63/37.29 +-Applying beta-rule and splitting (34), into two cases.
% 62.63/37.29 |-Branch one:
% 62.63/37.29 | (39) ~ (all_31_0_14 = 0)
% 62.63/37.29 |
% 62.63/37.29 +-Applying beta-rule and splitting (38), into two cases.
% 62.63/37.29 |-Branch one:
% 62.63/37.29 | (40) ~ (in(all_31_2_16, all_18_0_12) = 0)
% 62.63/37.29 |
% 62.63/37.29 | From (29) and (37) follows:
% 62.63/37.29 | (41) in(all_31_2_16, all_18_0_12) = 0
% 62.63/37.29 |
% 62.63/37.29 | Using (41) and (40) yields:
% 62.63/37.29 | (42) $false
% 62.63/37.29 |
% 62.63/37.29 |-The branch is then unsatisfiable
% 62.63/37.29 |-Branch two:
% 62.63/37.29 | (43) in(all_31_2_16, all_9_0_6) = 0 & ? [v0] : ? [v1] : (singleton(v0) = v1 & ordered_pair(v0, v1) = all_31_2_16 & in(v0, all_9_2_8) = 0)
% 62.63/37.29 |
% 62.63/37.29 | Applying alpha-rule on (43) yields:
% 62.63/37.29 | (44) in(all_31_2_16, all_9_0_6) = 0
% 62.63/37.29 | (45) ? [v0] : ? [v1] : (singleton(v0) = v1 & ordered_pair(v0, v1) = all_31_2_16 & in(v0, all_9_2_8) = 0)
% 62.63/37.29 |
% 62.63/37.29 | Instantiating formula (17) with all_31_2_16, all_9_0_6, 0, all_31_0_14 and discharging atoms in(all_31_2_16, all_9_0_6) = all_31_0_14, in(all_31_2_16, all_9_0_6) = 0, yields:
% 62.63/37.29 | (46) all_31_0_14 = 0
% 62.63/37.29 |
% 62.63/37.29 | Equations (46) can reduce 39 to:
% 62.63/37.29 | (47) $false
% 62.63/37.29 |
% 62.63/37.29 |-The branch is then unsatisfiable
% 62.63/37.29 |-Branch two:
% 62.63/37.29 | (48) ~ (all_31_1_15 = 0) | ! [v0] : ! [v1] : ( ~ (ordered_pair(v0, v1) = all_31_2_16) | ? [v2] : ? [v3] : (singleton(v0) = v3 & in(v0, all_9_2_8) = v2 & ( ~ (v3 = v1) | ~ (v2 = 0))))
% 62.65/37.29 |
% 62.65/37.29 +-Applying beta-rule and splitting (48), into two cases.
% 62.65/37.29 |-Branch one:
% 62.65/37.29 | (49) ~ (all_31_1_15 = 0)
% 62.65/37.29 |
% 62.65/37.29 | Equations (36) can reduce 49 to:
% 62.65/37.29 | (47) $false
% 62.65/37.29 |
% 62.65/37.29 |-The branch is then unsatisfiable
% 62.65/37.29 |-Branch two:
% 62.65/37.29 | (51) ! [v0] : ! [v1] : ( ~ (ordered_pair(v0, v1) = all_31_2_16) | ? [v2] : ? [v3] : (singleton(v0) = v3 & in(v0, all_9_2_8) = v2 & ( ~ (v3 = v1) | ~ (v2 = 0))))
% 62.65/37.29 |
% 62.65/37.29 +-Applying beta-rule and splitting (38), into two cases.
% 62.65/37.29 |-Branch one:
% 62.65/37.29 | (40) ~ (in(all_31_2_16, all_18_0_12) = 0)
% 62.65/37.29 |
% 62.65/37.29 | From (29) and (37) follows:
% 62.65/37.29 | (41) in(all_31_2_16, all_18_0_12) = 0
% 62.65/37.29 |
% 62.65/37.29 | Using (41) and (40) yields:
% 62.65/37.29 | (42) $false
% 62.65/37.29 |
% 62.65/37.29 |-The branch is then unsatisfiable
% 62.65/37.29 |-Branch two:
% 62.65/37.29 | (43) in(all_31_2_16, all_9_0_6) = 0 & ? [v0] : ? [v1] : (singleton(v0) = v1 & ordered_pair(v0, v1) = all_31_2_16 & in(v0, all_9_2_8) = 0)
% 62.65/37.29 |
% 62.65/37.29 | Applying alpha-rule on (43) yields:
% 62.65/37.29 | (44) in(all_31_2_16, all_9_0_6) = 0
% 62.65/37.29 | (45) ? [v0] : ? [v1] : (singleton(v0) = v1 & ordered_pair(v0, v1) = all_31_2_16 & in(v0, all_9_2_8) = 0)
% 62.65/37.29 |
% 62.65/37.29 | Instantiating (45) with all_73_0_23, all_73_1_24 yields:
% 62.65/37.29 | (58) singleton(all_73_1_24) = all_73_0_23 & ordered_pair(all_73_1_24, all_73_0_23) = all_31_2_16 & in(all_73_1_24, all_9_2_8) = 0
% 62.65/37.29 |
% 62.65/37.29 | Applying alpha-rule on (58) yields:
% 62.65/37.29 | (59) singleton(all_73_1_24) = all_73_0_23
% 62.65/37.29 | (60) ordered_pair(all_73_1_24, all_73_0_23) = all_31_2_16
% 62.65/37.29 | (61) in(all_73_1_24, all_9_2_8) = 0
% 62.65/37.29 |
% 62.65/37.29 | Instantiating formula (51) with all_73_0_23, all_73_1_24 and discharging atoms ordered_pair(all_73_1_24, all_73_0_23) = all_31_2_16, yields:
% 62.65/37.29 | (62) ? [v0] : ? [v1] : (singleton(all_73_1_24) = v1 & in(all_73_1_24, all_9_2_8) = v0 & ( ~ (v1 = all_73_0_23) | ~ (v0 = 0)))
% 62.65/37.29 |
% 62.65/37.29 | Instantiating (62) with all_82_0_26, all_82_1_27 yields:
% 62.65/37.29 | (63) singleton(all_73_1_24) = all_82_0_26 & in(all_73_1_24, all_9_2_8) = all_82_1_27 & ( ~ (all_82_0_26 = all_73_0_23) | ~ (all_82_1_27 = 0))
% 62.65/37.29 |
% 62.65/37.29 | Applying alpha-rule on (63) yields:
% 62.65/37.29 | (64) singleton(all_73_1_24) = all_82_0_26
% 62.65/37.29 | (65) in(all_73_1_24, all_9_2_8) = all_82_1_27
% 62.65/37.29 | (66) ~ (all_82_0_26 = all_73_0_23) | ~ (all_82_1_27 = 0)
% 62.65/37.29 |
% 62.65/37.29 | Instantiating formula (16) with all_73_1_24, all_82_0_26, all_73_0_23 and discharging atoms singleton(all_73_1_24) = all_82_0_26, singleton(all_73_1_24) = all_73_0_23, yields:
% 62.65/37.29 | (67) all_82_0_26 = all_73_0_23
% 62.65/37.29 |
% 62.65/37.29 | Instantiating formula (17) with all_73_1_24, all_9_2_8, all_82_1_27, 0 and discharging atoms in(all_73_1_24, all_9_2_8) = all_82_1_27, in(all_73_1_24, all_9_2_8) = 0, yields:
% 62.65/37.29 | (68) all_82_1_27 = 0
% 62.65/37.29 |
% 62.65/37.29 +-Applying beta-rule and splitting (66), into two cases.
% 62.65/37.29 |-Branch one:
% 62.65/37.29 | (69) ~ (all_82_1_27 = 0)
% 62.65/37.29 |
% 62.65/37.29 | Equations (68) can reduce 69 to:
% 62.65/37.29 | (47) $false
% 62.65/37.29 |
% 62.65/37.29 |-The branch is then unsatisfiable
% 62.65/37.29 |-Branch two:
% 62.65/37.29 | (71) ~ (all_82_0_26 = all_73_0_23)
% 62.65/37.29 |
% 62.65/37.29 | Equations (67) can reduce 71 to:
% 62.65/37.29 | (47) $false
% 62.65/37.29 |
% 62.65/37.29 |-The branch is then unsatisfiable
% 62.65/37.29 |-Branch two:
% 62.65/37.29 | (49) ~ (all_31_1_15 = 0)
% 62.65/37.29 | (74) all_31_0_14 = 0 & ? [v0] : ? [v1] : (singleton(v0) = v1 & ordered_pair(v0, v1) = all_31_2_16 & in(v0, all_9_2_8) = 0)
% 62.65/37.29 |
% 62.65/37.29 | Applying alpha-rule on (74) yields:
% 62.65/37.29 | (46) all_31_0_14 = 0
% 62.65/37.29 | (45) ? [v0] : ? [v1] : (singleton(v0) = v1 & ordered_pair(v0, v1) = all_31_2_16 & in(v0, all_9_2_8) = 0)
% 62.65/37.30 |
% 62.65/37.30 | Instantiating (45) with all_40_0_17, all_40_1_18 yields:
% 62.65/37.30 | (77) singleton(all_40_1_18) = all_40_0_17 & ordered_pair(all_40_1_18, all_40_0_17) = all_31_2_16 & in(all_40_1_18, all_9_2_8) = 0
% 62.65/37.30 |
% 62.65/37.30 | Applying alpha-rule on (77) yields:
% 62.65/37.30 | (78) singleton(all_40_1_18) = all_40_0_17
% 62.65/37.30 | (79) ordered_pair(all_40_1_18, all_40_0_17) = all_31_2_16
% 62.65/37.30 | (80) in(all_40_1_18, all_9_2_8) = 0
% 62.65/37.30 |
% 62.65/37.30 | From (46) and (33) follows:
% 62.65/37.30 | (44) in(all_31_2_16, all_9_0_6) = 0
% 62.65/37.30 |
% 62.65/37.30 | Instantiating formula (27) with all_31_1_15, all_31_2_16 and discharging atoms in(all_31_2_16, all_9_0_6) = 0, yields:
% 62.65/37.30 | (82) all_31_1_15 = 0 | ~ (in(all_31_2_16, all_18_0_12) = all_31_1_15) | ! [v0] : ! [v1] : ( ~ (ordered_pair(v0, v1) = all_31_2_16) | ? [v2] : ? [v3] : (singleton(v0) = v3 & in(v0, all_9_2_8) = v2 & ( ~ (v3 = v1) | ~ (v2 = 0))))
% 62.65/37.30 |
% 62.65/37.30 +-Applying beta-rule and splitting (82), into two cases.
% 62.65/37.30 |-Branch one:
% 62.65/37.30 | (83) ~ (in(all_31_2_16, all_18_0_12) = all_31_1_15)
% 62.65/37.30 |
% 62.65/37.30 | From (29) and (32) follows:
% 62.65/37.30 | (84) in(all_31_2_16, all_18_0_12) = all_31_1_15
% 62.65/37.30 |
% 62.65/37.30 | Using (84) and (83) yields:
% 62.65/37.30 | (42) $false
% 62.65/37.30 |
% 62.65/37.30 |-The branch is then unsatisfiable
% 62.65/37.30 |-Branch two:
% 62.65/37.30 | (86) all_31_1_15 = 0 | ! [v0] : ! [v1] : ( ~ (ordered_pair(v0, v1) = all_31_2_16) | ? [v2] : ? [v3] : (singleton(v0) = v3 & in(v0, all_9_2_8) = v2 & ( ~ (v3 = v1) | ~ (v2 = 0))))
% 62.65/37.30 |
% 62.65/37.30 +-Applying beta-rule and splitting (86), into two cases.
% 62.65/37.30 |-Branch one:
% 62.65/37.30 | (36) all_31_1_15 = 0
% 62.65/37.30 |
% 62.65/37.30 | Equations (36) can reduce 49 to:
% 62.65/37.30 | (47) $false
% 62.65/37.30 |
% 62.65/37.30 |-The branch is then unsatisfiable
% 62.65/37.30 |-Branch two:
% 62.65/37.30 | (51) ! [v0] : ! [v1] : ( ~ (ordered_pair(v0, v1) = all_31_2_16) | ? [v2] : ? [v3] : (singleton(v0) = v3 & in(v0, all_9_2_8) = v2 & ( ~ (v3 = v1) | ~ (v2 = 0))))
% 62.65/37.30 |
% 62.65/37.30 | Instantiating formula (51) with all_40_0_17, all_40_1_18 and discharging atoms ordered_pair(all_40_1_18, all_40_0_17) = all_31_2_16, yields:
% 62.65/37.30 | (90) ? [v0] : ? [v1] : (singleton(all_40_1_18) = v1 & in(all_40_1_18, all_9_2_8) = v0 & ( ~ (v1 = all_40_0_17) | ~ (v0 = 0)))
% 62.65/37.30 |
% 62.65/37.30 | Instantiating (90) with all_69_0_44, all_69_1_45 yields:
% 62.65/37.30 | (91) singleton(all_40_1_18) = all_69_0_44 & in(all_40_1_18, all_9_2_8) = all_69_1_45 & ( ~ (all_69_0_44 = all_40_0_17) | ~ (all_69_1_45 = 0))
% 62.65/37.30 |
% 62.65/37.30 | Applying alpha-rule on (91) yields:
% 62.65/37.30 | (92) singleton(all_40_1_18) = all_69_0_44
% 62.65/37.30 | (93) in(all_40_1_18, all_9_2_8) = all_69_1_45
% 62.65/37.30 | (94) ~ (all_69_0_44 = all_40_0_17) | ~ (all_69_1_45 = 0)
% 62.65/37.30 |
% 62.65/37.30 | Instantiating formula (16) with all_40_1_18, all_69_0_44, all_40_0_17 and discharging atoms singleton(all_40_1_18) = all_69_0_44, singleton(all_40_1_18) = all_40_0_17, yields:
% 62.65/37.30 | (95) all_69_0_44 = all_40_0_17
% 62.65/37.30 |
% 62.65/37.30 | Instantiating formula (17) with all_40_1_18, all_9_2_8, all_69_1_45, 0 and discharging atoms in(all_40_1_18, all_9_2_8) = all_69_1_45, in(all_40_1_18, all_9_2_8) = 0, yields:
% 62.65/37.30 | (96) all_69_1_45 = 0
% 62.65/37.30 |
% 62.65/37.30 +-Applying beta-rule and splitting (94), into two cases.
% 62.65/37.30 |-Branch one:
% 62.65/37.30 | (97) ~ (all_69_1_45 = 0)
% 62.65/37.30 |
% 62.65/37.30 | Equations (96) can reduce 97 to:
% 62.65/37.30 | (47) $false
% 62.65/37.30 |
% 62.65/37.30 |-The branch is then unsatisfiable
% 62.65/37.30 |-Branch two:
% 62.65/37.30 | (99) ~ (all_69_0_44 = all_40_0_17)
% 62.65/37.30 |
% 62.65/37.30 | Equations (95) can reduce 99 to:
% 62.65/37.30 | (47) $false
% 62.65/37.30 |
% 62.65/37.30 |-The branch is then unsatisfiable
% 62.65/37.30 % SZS output end Proof for theBenchmark
% 62.71/37.30
% 62.71/37.30 36723ms
%------------------------------------------------------------------------------